# Training Physics-Informed Neural Networks via Multi-Task Optimization for Traffic Density Prediction

arXiv: https://arxiv.org/abs/2307.03920 · HTML: https://mlsanity.com/paper/2307.03920/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 8 Jul 2023.

## Builds on (most cited first, 8 of 8)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Evolutionary Multitask Optimization: a Methodological Overview, Challenges and Future Research Directions](https://mlsanity.com/paper/2102.02558/) (2021)
- [Multi-task Optimization Based Co-training for Electricity Consumption Prediction](https://mlsanity.com/paper/2205.15663/) (2022)
- [A Novel DNN Training Framework via Data Sampling and Multi-Task Optimization](https://mlsanity.com/paper/2007.01016/) (2020)

## Built on by (most cited first, 2 of 2)

- [Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metrics](https://mlsanity.com/paper/2402.11126/) (2024)
- [Real-Time Traffic Density Estimation: A Hybrid Computer Vision and Predictive Machine Learning Pipeline](https://mlsanity.com/paper/2610.14326/) (2026)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into the training of the neural network (NN) based on such a data set. In PINNs, the NN acts as the solution approximator for the PDE while the PDE acts as the prior knowledge to guide the NN training, leading to the desired generalization performance of the NN when facing the limited availability of training data. However, training PINNs is a non-trivial task largely due to the complexity of the loss composed of both NN and physical law parts. In this work, we propose a new PINN training framework based on the multi-task optimization (MTO) paradigm. Under this framework, multiple auxiliary tasks are created and solved together with the given (main) task, where the useful knowledge from solving one task is transferred in an adaptive mode to assist in solving some other tasks, aiming to uplift the performance of solving the main task. We implement the proposed framework and apply it to train the PINN for addressing the traffic density prediction problem. Experimental results demonstrate that our proposed training framework leads to significant performance improvement in comparison to the traditional way of training the PINN.